1. Field of the Invention
The invention pertains to the field of software, computer systems and related methods including models that operate through the use of finite analysis, finite volume, and/or finite difference techniques.
2. Description of the Related Art
Finite element, finite volume, and finite difference modeling techniques can generally be described as mathematical approximations of often-complex problems that represent physical behavior. The mathematical models are useful in designing physical apparatus or systems and in predicting the behavior of existing apparatus or systems. These models use a mesh or grid that is superimposed over the system being studied to provide a plurality of cells or elements. These elements may be modeled in multiple dimensions, for example, one, two, or three dimensions. Mathematical equations that represent or approximate physical or quantitative behavior are applied to each cell with the resultant formation of a system of equations that are expressed as matrices, and that are solved using generally known techniques of linear algebra. Such mathematical techniques commonly involve iterating through a set of equations until a threshold convergence is achieved, i.e., until the difference between successive iterations through a system of mathematical approximations becomes so small that it is suitably negligible with respect to the exact or rigorous solution of the system of equations being modeled. The term “finite analysis” is hereby defined to include finite element, finite volume and finite difference models.
A variety of patents have issued on various finite element and finite difference techniques. For example, U.S. Pat. Nos. 5,956,500 and 5,901,072 pertain to a method for incorporating boundary conditions into a finite analysis model. These patents disclose generating a finite analysis model having a finite element shim interposed between a test bar and a ground, where the characteristics of the shim are selected based upon measured natural frequencies of the test bar. U.S. Pat. No. 5,768,156 addresses a method of automatic mesh generation for finite analysis. The meshes are generated using whisker chords to form all-hexahedral elements. Similarly, U.S. Pat. No. 5,731,817 pertains to a system that generates a hexahedron mesh and then performs finite analysis on the mesh. U.S. Pat. No. 5,581,489 discloses a model generator including data input for an object to be modeled, a material information generator providing material properties for the object being modeled, a mesh processor for generating a mesh, and an output generator coupled with a finite analysis processor. U.S. Pat. Nos. 5,553,206 and 5,315,537 pertain to automatic mesh generation systems.
Finite analysis programs that provide solutions to specific problems are commercially available. For example, ABAQUS® is available from Hibbitt, Karlsson and Sorenson, Inc., of Pawtucket, R.I. to model structural mechanics and nonlinear heat transfer. ANSYS® is available from Ansys, Inc., of Canonsburg, Pa. to model structural mechanics and heat transfer. ASTMA is public domain software available from the National Aeronautics and Space Administration (NASA) that models heat transfer and ablation. I-DEAS is available from Structural Dynamics Research Corporation of Milford, Ohio to provide pre and post-processing images of the model. SINDA from Network Analysis, Inc., of Chandler, Arizona models heat transfer. TEX CHEM models chemical reactions and chemical equilibrium. RECESS is a program developed by Thiokol Propulsion of Brigham City, Utah to model internal ballistics. CDCA is a computational fluid dynamics program developed by Pennsylvania State University to model crack combustion where a fracture in a propellant affects burn condition. CCM is a similar computational fluid dynamics program available in the public domain, and is available from the Air Force Research Laboratory (AFRL).
Many specific examples of the need for finite analysis programs exist, for example, in the field of rocketry and missile maintenance. In fact, the commercial finite analysis programs that are mentioned above have many specific applications in this field. For example, the public domain ASTMA program and derivatives thereof can be used to model the burning away of material from a rocket engine nozzle.
A problem exists in the field of finite analysis modeling because engineering specialties do not encompass a wide array of specialized problems that are presented by complex physical situations. For example, the burning of a solid fuel rocket motor presents a multifaceted problem including structural mechanics, material properties, internal ballistics, chemical reactions, heat transfer, crack combustion, and fracture mechanics. An engineer who is modeling only one of these problems using a commercially available or proprietary finite analysis program for this purpose may require a full year just to become proficient at using the package. Typically, such an engineer is not trained in more than one or two of the specialty problem areas and is often incapable of running models in areas outside his or her area of expertise. Very few, if any, engineers succeed in acquiring the training that is required to model all aspects of this problem, and a team of modelers often is required to produce modeling results through a laborious process involving the transfer of model results between different engineers and/or finite analysis codes.
It is typical in the finite analysis art that there exist separate programs to model computational fluid dynamics, structural mechanics, heat transfer, internal ballistics, etc. This segregation of problems exists, in part, due to the lack of overlap in specialty areas as described above, but it also exists because the situations encountered for actual modeling purposes are very diverse and require flexibility if the model is to have optimum results. A great deal of effort may be expended to develop a comprehensive model where the usefulness of the model diminishes with its complexity.
The foregoing problem is normally addressed by a sharing of data between engineers or engineering groups that encompass multiple specialties. This sharing of data leads to additional problems. An engineer receiving model results from another engineer for further processing does not necessarily understand the model results that he or she has received, and this circumstance can lead to computational error. For example, the preceding engineer may provide results from a less thorough model than is required for optimum results in subsequent calculations, or problems may arise through the nodes of meshes being at different locations when data is passed from a first model to a second model.
Special problems also arise when an engineer receives prior calculation results and uses them as input in a subsequent model addressing a different problem because subsequent calculation results may affect input for the prior model. For example, an internal ballistics program may be used to calculate internal pressures in a solid fuel rocket motor. These pressures are subsequently used in structural mechanics calculations where the rocket fuel deforms in a visco-elastic manner. The volume changes from the structural mechanics solution have significant effects upon the internal ballistics results which, in turn, affect the structural mechanics model. Thus, a repetitive sharing and transfer of computational results is required from successive iterations until the effects of the separate programs upon one another between different runs become negligible. Furthermore, the respective modelers may even be unaware that their individual model or an aspect of their model results can affect other models that provide results including input data for subsequent models.